On Neutrosophic Ideals of B-algebra
Abstract
This paper presents a comprehensive study of neutrosophic concepts in B-algebras, focusing on several types of neutrosophic ideals including neutrosophic ideals, neutrosophic near ideals, neutrosophic Ns-ideals, neutrosophic power ideals, and neutrosophic near power ideals. The paper establishes and proves multiple results, such as: every neutrosophic B-algebra is both a neutrosophic near ideal and a neutrosophic Ns-ideal; every neutrosophic ideal and every neutrosophic near ideal of a B-algebra is a neutrosophic Ns-ideal; every neutrosophic regular set in a B-algebra is a neutrosophic Ns-ideal; every neutrosophic B-algebra is also a neutrosophic power ideal; every neutrosophic ideal, near ideal, and regular set in a B-algebra is a neutrosophic power ideal; every neutrosophic power ideal is a neutrosophic Ns-power ideal; and similarly, every neutrosophic B-algebra, near ideal, and regular set is a neutrosophic Ns-power ideal. In addition to these findings, the paper explores the structural relationships and properties among these different types of neutrosophic ideals, providing a deeper understanding of their significance within the framework of B-algebras. These results contribute to the theoretical development of neutrosophic algebraic structures and may serve as a foundation for future applications in logic, information systems, and decision-making models involving indeterminacy.
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